Properties

Label 34496bw
Number of curves $1$
Conductor $34496$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bw1")
 
E.isogeny_class()
 

Elliptic curves in class 34496bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34496.d1 34496bw1 \([0, 0, 0, 392, -686]\) \(884736/539\) \(-4058419904\) \([]\) \(27648\) \(0.53288\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 34496bw1 has rank \(1\).

Complex multiplication

The elliptic curves in class 34496bw do not have complex multiplication.

Modular form 34496.2.a.bw

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} - q^{5} + 6 q^{9} + q^{11} - 4 q^{13} + 3 q^{15} - 2 q^{17} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display